Highest Common Factor of 543, 900, 121 using Euclid's algorithm
Created By : Jatin Gogia
Reviewed By : Rajasekhar Valipishetty
Last Updated : Apr 06, 2023
HCF Calculator using the Euclid Division Algorithm helps you to find the Highest common factor (HCF) easily for 543, 900, 121 i.e. 1 the largest integer that leaves a remainder zero for all numbers.
HCF of 543, 900, 121 is 1 the largest number which exactly divides all the numbers i.e. where the remainder is zero. Let us get into the working of this example.
Consider we have numbers 543, 900, 121 and we need to find the HCF of these numbers. To do so, we need to choose the largest integer first and then as per Euclid's Division Lemma a = bq + r where 0 ≤ r ≤ b
Highest common factor (HCF) of 543, 900, 121 is 1.
HCF(543, 900, 121) = 1
HCF of 543, 900, 121 using Euclid's algorithm
Highest common factor or Highest common divisor (hcd) can be calculated by Euclid's algotithm.
Highest common factor (HCF) of 543, 900, 121 is 1.
Highest Common Factor of 543,900,121 is 1
Step 1: Since 900 > 543, we apply the division lemma to 900 and 543, to get
900 = 543 x 1 + 357
Step 2: Since the reminder 543 ≠ 0, we apply division lemma to 357 and 543, to get
543 = 357 x 1 + 186
Step 3: We consider the new divisor 357 and the new remainder 186, and apply the division lemma to get
357 = 186 x 1 + 171
We consider the new divisor 186 and the new remainder 171,and apply the division lemma to get
186 = 171 x 1 + 15
We consider the new divisor 171 and the new remainder 15,and apply the division lemma to get
171 = 15 x 11 + 6
We consider the new divisor 15 and the new remainder 6,and apply the division lemma to get
15 = 6 x 2 + 3
We consider the new divisor 6 and the new remainder 3,and apply the division lemma to get
6 = 3 x 2 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 3, the HCF of 543 and 900 is 3
Notice that 3 = HCF(6,3) = HCF(15,6) = HCF(171,15) = HCF(186,171) = HCF(357,186) = HCF(543,357) = HCF(900,543) .
We can take hcf of as 1st numbers and next number as another number to apply in Euclidean lemma
Step 1: Since 121 > 3, we apply the division lemma to 121 and 3, to get
121 = 3 x 40 + 1
Step 2: Since the reminder 3 ≠ 0, we apply division lemma to 1 and 3, to get
3 = 1 x 3 + 0
The remainder has now become zero, so our procedure stops. Since the divisor at this stage is 1, the HCF of 3 and 121 is 1
Notice that 1 = HCF(3,1) = HCF(121,3) .
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Frequently Asked Questions on HCF of 543, 900, 121 using Euclid's Algorithm
1. What is the Euclid division algorithm?
Answer: Euclid's Division Algorithm is a technique to compute the Highest Common Factor (HCF) of given positive integers.
2. what is the HCF of 543, 900, 121?
Answer: HCF of 543, 900, 121 is 1 the largest number that divides all the numbers leaving a remainder zero.
3. How to find HCF of 543, 900, 121 using Euclid's Algorithm?
Answer: For arbitrary numbers 543, 900, 121 apply Euclid’s Division Lemma in succession until you obtain a remainder zero. HCF is the remainder in the last but one step.
